Transcript Equations of Circles

4 minutes
Warm-Up
1. Graph the equation x2 - 8x – y + 20 = 0.
Label the vertex, focus, and directrix.
9.3.1 Circles
Objectives:
•Write an equation for a circle given sufficient
information
•Given an equation of a circle, graph it and label the
radius and the center
Standard Equation of a Circle
OP = r
(x  0)2  (y  0)2  r
P(x,y)
r
x2  y 2  r
x2  y2  r2
O
Standard Equation of a Circle
An equation for the circle with its center at (0,0)
and a radius of r is
x2  y2  r2
Example 1
Write the standard equation of the circle
whose center is at the origin and whose
radius is 4. Sketch the graph.
x2  y2  r2
4
x2  y2  42
x2  y2  16
2
-4
-2
-2
-4
2
4
Standard Equation of a Circle
The standard equation for a translated circle is
(x – h)2 + (y – k)2 = r2
center: (h, k)
radius: r
Example 2
Write the standard equation of the circle
graphed below.
(x  h)2  (y  k)2  r2
8
(x  (2))2  (y  3)2  42
6
4
(x  2)2  (y  3)2  16
2
-8 -6 -4
-2
Practice
Write the standard equation of a circle with
the following center and radius.
1) C(0,0) radius: 9
2) C(2,3) radius: 5
3) C(-5,2) radius: 4
Practice
Graph each equation. Label the center and
radius.
1) x2 + y2 = 25
2) (x – 2)2 + y2 = 4
3) (x + 4)2 + (y – 3)2 = 49
Homework
p.583 #11-21 odds; 33-39 odds
4 minutes
Warm-Up
1. Graph the equation x2 + (y + 3)2 = 16. Label
the center and the radius.
9.3.2 Circles
Objectives:
•Write an equation for a circle given sufficient
information
•Given an equation of a circle, graph it and label the
radius and the center
Example 1
Write the standard equation for the circle
given by x2 + y2 – 12x – 2y - 8 = 0. State the
coordinates of its center and give its radius.
x2  y2  12x  2y  8  0
x2  12x  y2  2y  8
(x2  12x  36)  ( y2  2y  1)  8  36  1
(x  6)2  (y  1)2  45
Center: (6,1)
Radius:
45  3 5
Example 2
Write the standard equation for the circle
given by x2 + y2 + 6x – 4y - 3 = 0. State the
coordinates of its center and give its radius.
Then sketch the graph.
x2  y2  6x  4y  3  0
x2  6x  y2  4y  3
(x2  6x  9)  ( y2  4y  4)  3  9  4
(x  3)2  (y  2)2  16
8
6
Center: (-3,2)
Radius:
4
16  4
2
-8 -6 -4
-2
Practice
Write the standard equation for the circle
given by x2 + y2 - 2x + 2y - 7 = 0. State the
coordinates of its center and give its radius.
Then sketch the graph.
Homework
p.583 #25,27,41,43,49,51,55